Jahn second-order

The cyclopentadienyl radical and the cyclopentadienyl cation are two well-known Jahn-Teller problems The traditional Jahn-Teller heatment starts at the D k symmetry, and looks for the normal modes that reduce the symmetry by first-01 second-order vibronic coupling. A Longuet-Higgins treatment will search for anchors that may be used to form the proper loop. The coordinates relevant to this approach are reaction coordinates. 

It was shown by several workers that in this case the first-order Jahn-Teller distortion is due to an ej vibration, and that the second-order distortion vanishes. Therefore, in terms of simple Jahn-Teller theoi, the moat around the symmetric point should be a Mexican hat type, without secondary minima. This expectation was borne out by high-level quantum chemical calculations, which showed that the energy difference between the two expected C2v structures ( A2 and Bi) were indeed very small [73]. 

Recently, a symmetry rule for predicting stable molecular shapes has been developed by Pearson Salem and Bartell" . This rule is based on the second-order, or pseudo, Jahn-Teller effect and follows from the earlier work by Bader . According to the symmetry rule, the symmetries of the ground state and the lowest excited state determine which kind of nuclear motion occurs most easily in the ground state of a molecule. Pearson has shown that this approximation is justified in a large variety of inorganic and small organic molecules. 

A hysteresis cycle in the molar susceptibility measurements has been observed for [Ni2(Medpt)2(N3)2(/r-N3)2] (883). This has been ascribed to a phase transition caused by an asymmetrization process of the rhombus-like centrosymmetric [Ni-(N3)2-Ni] core that occurs with falling temperature. The asymmetrization transition can be explained in terms of a second-order Jahn-Teller distortion, taking into account the local symmetry of the dinuclear [Ni-(N3)2-Ni] entity (D2h, rhombic symmetry) before the arrangement.2128... 

The most recent theoretical study, by Alhrichs and co-workers, deals with the di(phosphino)carbene Id and (phosphino) (phosphonio)carbenes Ie,f.16 The optimized geometry of the di(phosphino)carbene Id is weakly bent (PCP angle 160.5°) and highly unsymmetrical Only one of the phosphorus centers (P1) is in a planar environment, and it is much more closely bonded to the carbenic center than the other one (P1C 1.533 and P2C 1.765 A). The atomic charges (P1 +1.0, C -0.8, P2 +0.6) indicate that the short P bond is a double bond reinforced by Coulombic attraction, while the nature of the molecular orbitals revealed a slight delocalization of the carbene lone pair into the low-lying a (P-N) orbitals of the two phosphino substituents. The distortion from the symmetrical structure can be viewed as a second-order Jahn-Teller effect. 

Wade expanded the 1971 hypothesis to incorporate metal hydrocarbon 7T complexes, electron-rich aromatic ring systems, and aspects of transition metal cluster compounds [a parallel that had previously been noted by Corbett 19) for cationic bismuth clusters]. Rudolph and Pretzer chose to emphasize the redox nature of the closo, nido, and arachno interconversions within a given size framework, and based the attendant opening of the deltahedron after reduction (diagonally downward from left to right in Fig. 1) on first- and second-order Jahn-Teller distortions 115, 123). Rudolph and Pretzer have also successfully utilized the author s approach to predict the most stable configuration of SB9H9 (1-25) 115) and other thiaboranes. 

In the examples predated in the text, the distortions from high symmetry which lead to stabilization of the molecular shapes are those in which the HOMO and LUMO of the highly symmetric molecules both become the completely symmetric representations of the distorted molecules, i.e. a. There is a general rule which deals wi+h this phenomenon in a detailed way called the second-order Jahn-Teller effect but nt they say. anotlv . ... 

Fig. 1. Conical intersection surface topologies (top), and Renner-Teller surface topologies (bottom). Top left is a generic circular cone, such as is obtained from a Jahn-Teller problem involving only the linear vibronic coupling. Top right is a sloped conical intersection obtained in a general vibronic coupling problem where all three linear vibronic coupling constants are different. Bottom left to right show type-1, -II, -III Renner-Teller surfaces. These are obtained when only second-order vibronic coupling is included.

As noted previously, the outstanding success of orbital symmetry rules in organic chemistry (75, 242) has led to many attempts to extend these rules to organometallic chemistry and metal-catalyzed processes. These qualitative analyses based on the principle of conservation of orbital symmetry or second-order Jahn-Teller effects have been reviewed extensively (91, 142, 143, 173, 175, 179, 221, 225) and will not be considered in any detail here. 

The preceding three reduced molybdenum clusters indicate that rhomboidal cluster units are common among this kind of oxide, and the Mo-Mo distances in the cluster units are dependent on CVE assignable to the Mo4 units. MO calculations on Mo4 molecular cluster compounds containing 10 CVE and 8 CVE have shown that the 8-electron clusters distort from a second-order Jahn-Teller effect (116). Such a distortion has been observed in the 8-electron W4(OEt)16 (117). 

TL OEt) ]224 with distortions due to M—M bonding. Crystal structure analysis of [W4(OEt)i6] (Figure 22) reveals the presence of two short W—W bonds (2.645 and 2.76 A) and two long bonds of 2.93 A. In this structure, there is a total of five possible W—W interactions, and thus, to form five bonds of order one, ten electrons are required. Only eight metal electrons are available for metal-metal bonding, which leads to the observed distortions. It has been suggested that this distortion results from a novel second order Jahn-Teller effect.225... 

Thus while the Jahn-Teller theorem is generally invoked to account for the distorted octahedral geometries of the copper(II) ion, in terms of the first-order vibronic coupling the extension of the coupling to some second-order effects also allows some rationalization of the tetrahedral and five-coordinate geometries of the copper(II) ion.1063-1067... 

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